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5 results on '"likelihood ratio/score function method"'

2. Efficient Design and Sensitivity Analysis of Control Charts Using Monte Carlo Simulation.

Author

Michael C. Fu and Jian-Qiang Hu

Subjects
QUALITY control charts, MONTE Carlo method, EXPERIMENTAL design, SIMULATION methods & models, STATISTICAL sampling, PROBABILITY measures, TOTAL quality management, MULTIVARIATE analysis, STATISTICAL process control, INDUSTRIAL design management, INDUSTRIAL costs, ESTIMATION theory, MANAGEMENT
Abstract

The design of control charts in statistical quality control addresses the optimal selection of the design parameters (such as the sampling frequency and the control limits) and includes sensitivity analysis with respect to system parameters (such as the various process parameters and the economic costs of sampling). The advent of more complicated control chart schemes has necessitated the use of Monte Carlo simulation in the design process, especially in the evaluation of performance measures such as average run length. In this paper, we apply two gradient estimation procedures--perturbation analysis and the likelihood ratio/score function method to derive estimators that can be used in gradient-based optimization algorithms and in sensitivity analysis when Monte Carlo simulation is employed. We illustrate the techniques on a general control chart that includes the Shewhart chart and the exponentially-weighted moving average chart as special cases. Simulation examples comparing the estimators with each other and with "brute force" finite differences demonstrate the possibility of significant variance reduction in settings of practical interest. [ABSTRACT FROM AUTHOR]

Published
1999
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3. Markov models for digraph panel data: Monte Carlo-based derivative estimation

Author

Schweinberger, Michael and Snijders, Tom A.B.

Subjects
*MARKOV processes, *MONTE Carlo method, *MATHEMATICAL statistics, *MATHEMATICAL models
Abstract

Abstract: A parametric, continuous-time Markov model for digraph panel data is considered. The parameter is estimated by the method of moments. A convenient method for estimating the variance–covariance matrix of the moment estimator relies on the delta method, requiring the Jacobian matrix—that is, the matrix of partial derivatives—of the estimating function. The Jacobian matrix was estimated hitherto by Monte Carlo methods based on finite differences. Three new Monte Carlo estimators of the Jacobian matrix are proposed, which are related to the likelihood ratio/score function method of derivative estimation and have theoretical and practical advantages compared to the finite differences method. Some light is shed on the practical performance of the methods by applying them in a situation where the true Jacobian matrix is known and in a situation where the true Jacobian matrix is unknown. [Copyright &y& Elsevier]

Published
2007
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4. Markov models for digraph panel data

Author

Tom A. B. Snijders, Michael Schweinberger, and Sociology/ICS

Subjects
Statistics and Probability, Monte Carlo method, variance reduction, gradient estimation, Control variates, Markov model, control variates, Matrix (mathematics), symbols.namesake, continuous-time Markov process, Calculus, likelihood ratio/score function method, Applied mathematics, SENSITIVITY ANALYSIS, Mathematics, Applied Mathematics, COMPUTER-SIMULATION MODELS, Estimator, Computational Mathematics, Computational Theory and Mathematics, Jacobian matrix and determinant, symbols, SOCIAL NETWORKS, Likelihood function, Matrix method, digraphs
Abstract

A parametric, continuous-time Markov model for digraph panel data is considered. The parameter is estimated by the method of moments. A convenient method for estimating the variance-covariance matrix of the moment estimator relies on the delta method, requiring the Jacobian matrix-that is, the matrix of partial derivatives-of the estimating function. The Jacobian matrix was estimated hitherto by Monte Carlo methods based on finite differences. Three new Monte Carlo estimators of the Jacobian matrix are proposed, which are related to the likelihood ratio/score function method of derivative estimation and have theoretical and practical advantages compared to the finite differences method. Some light is shed on the practical performance of the methods by applying them in a situation where the true Jacobian matrix is known and in a situation where the true Jacobian matrix is unknown. (c) 2006 Elsevier B.V. All rights reserved.

Published
2007

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